The present invention relates to the materials arts. It particularly relates to the analysis and estimation of fatigue life limited by crack formation and crack growth in materials undergoing applied stresses, especially rubber materials, and will be described with particular reference thereto. However, the invention will also find application in the analysis of other types of structural defects, and is furthermore applicable to materials other than rubbers that are undergoing mechanical stresses.
Models for predicting fatigue life in rubber follow two basic approaches. One approach focuses on predicting crack initiation life, given the history of at-a-point quantities such as stress and strain. The other approach, based on ideas from fracture mechanics, focuses on predicting the propagation of a particular crack, given the energy release rate history of the crack.
Several researchers have applied at-a-point quantities for life predictions in tires and other rubber parts. The quantities investigated have included maximum principal strain or stretch, maximum shear strain, octahedral shear strain, and total strain energy density. For incompressible materials, the total strain energy density is the same as the deviatoric strain energy density. These approaches generally assume that a unique relationship exists between the strain energy density and crack initiation life. While many in the rubber industry have used strain energy density as a predictive parameter for fatigue life, the range of validity of this approach under conditions typically experienced by parts in service has not been adequately investigated.
Fatigue life analysis methods based on fracture mechanics typically presuppose the existence of an initial xe2x80x9ctestxe2x80x9d crack and estimate its propagation under the strain history using iterative finite element analysis methods. Fatigue life is estimated by repeating the finite element analysis for a large plurality of test cracks with different sizes and orientations which are representative of the initial flaws believed to be present in the material. This approach is computationally expensive because each potential failure mode (i.e., test crack) requires its own finite element mesh and analysis. Furthermore, the crack propagation approach requires a priori knowledge of the initial location and state of the crack that causes the final failure. Often, this information is not available, and indeed is the very information the designer needs to predict.
The present invention contemplates an improved fatigue life estimation method which overcomes the aforementioned limitations and others.
According to one aspect of the invention, a method for estimating fatigue life for a material is disclosed. A multiaxial strain cycle is received that is described by a strain tensor that is a function of time. A hyperelastic constitutive model corresponding to the material is received. A fatigue crack growth curve is obtained. A cracking energy density is calculated based on the constitutive model and the multiaxial strain cycle. The cracking energy density is a function of material plane and indicates the portion of the total elastic strain energy density that is available to be released on a selected material plane. A cracking plane is determined based upon the cracking energy density. A fatigue life is estimated based on the cracking plane and the fatigue crack growth curve.
According to another aspect of the invention, a method for identifying a cracking plane in an elastic material under the action of a tensile multiaxial strain history is disclosed. A cracking energy density Wc is calculated for a material plane. The cracking energy density is incrementally defined by,
dWc={overscore ("sgr")}xc2x7d{overscore (xcex5)}
with
{overscore ("sgr")}="sgr"{overscore (r)}={overscore (r)}T"sgr", d{overscore (xcex5)}=dxcex5{overscore (r)}
where dWc is the incremental cracking energy density, "sgr" is the stress tensor, xcex5 is the strain tensor, and {overscore (r)} is a unit vector normal to the material plane. Calculating the cracking energy density Wc is repeated for a selected set of material planes. The cracking plane is identified based on the cracking energy density calculations.
According to yet another aspect of the invention, a program storage medium is readable by a computer and embodying one or more instructions executable by the computer to perform a method for estimating a fatigue life in a material that undergoes a strain history. The method includes the steps of defining a plurality of spatial planes that collectively represent the material planes; calculating cracking energy densities corresponding to the plurality of spatial planes wherein the cracking energy density of a spatial plane indicates the energy available to propagate a crack in that spatial plane; and estimating the fatigue life based on the calculated cracking energy densities.
Numerous advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiment.